Hi op,
I am a regular foster mum for dogs. 2 of my own dogs were rescued. One purchased. The oldest was purchased. The middle and baby were Foster then we decided to adopt. I would adopt them all but we don't have room 
Adoption is great. It's absolutely not for everyone. And that's OK. It took me a while to be able to cope with it. Dp was a natural.
The vast majority of dogs we get in through Foster, have fairly big problems. As a Fosterer, we work with behaviourists and trainers and vets, but sometimes the problems just need to managed rather than fixed. Some are just training issues, where they haven't had any.
The first few months with a new adopted dog, can be far more stressful than a puppy imo.
Middle dog, came to me as a Foster with 2 sisters who were abandoned in December 2019. About 5 weeks old. They were easier than alot of our older Foster dogs.
Our latest addition could be anything from an actual poodle, to a cavapoo/cavapoochon, cockapoo. No chip so can't trace her. She is actually quite nonchalant about people. She is super easy. She seems toilet trained on the whole. Quite independent. Happy to sleep alone or with the other dogs. Sleeps through etc. But my understand of poodle crosses (especially miniature or toy) is that they are usually quite clingy. Our best guess is that she was about 12 weeks old, when she arrived, as per the vet. She has slotted straight in and life is no different to when we had 3. Apart from she can't be walked yet, due to injections. So she stays with dp. While I take them. She currently snoozing on the wood floors near the older 2.
One of our fosters, who has been now been adopted, has been working with a behaviourist for 3 years. Still an escape artist that likes to chase cars. He lives with someone with a very secure garden that backs into woods and can't be walked off lead at all.
Many have temporary problems. That then present again when they go to a permanent homes. You can't gain a dogs trust while making them understand they won't be here permanently and they regress. Most are OK after a few months but need you to keep up with the schedule. Some go to their new home with no problems, at all. You can't tell.
I haven't had a nightmare puppy. Which I think is a mixture of luck and having behaviourists on hand to help. The oldest which we got from a breeder came home at 12 weeks old and was easy too. Occasional accidents but slept through from night 4. I have had puppies from breeders prior to this who were all fairly good too.
So please dont assume an older rescue will be easier than a puppy. But if you go to a breeder I wouldn't recommend a poodle Cross. Even though our girl seems great, they are usually poorly bred. Finding a good breeder poodle crosses is minefield. And honestly, they usually look like unclipped poodles. Which is why we couldn't guess what our is, they are all very alike in looks. They are often mixed with working dogs and can be hard work. Cavaliers have heart problems, which isn't guaranteed to not be present in a cavapoo. They are also not gaurenteed to not shed. Their coats also take a lot of grooming, especially if they don't shed. I won't be fostering any puppies until we move as I can't part with them. 
You can wait for a rescue puppy but finding one that fits your wants, may mean waiting for ages. Years. We have had 2 in 2 years and the latest isn't what we would have picked. But that's also because me and dp have done extra work offered by the rescue. But also because we have been able to drop everything and go. When we fostered the 3 sisters, we got a call on the 18th December. Drove a 10 hour round trip to get them on the 19th, and rearranged our Christmas plans so they were not over whelmed. This latest one, I was called on the sunday morning, spoke to dp, kids went to my parents for the afternoon/night and we went that afternoon. My kids are older but we like to settle them in with a quiet house for the first night.
Its a small rescue that I work with. Its obviously, very different if it's a big rescue. They will look after the puppies and have a wait list, not sure if that makes it easier or harder. For small rescues, those willing to Foster tend to be at the front of the queue. The vast majority are fostered, then adopted by the Foster family. Again, you don't know what you are getting though. People surrendering their dogs often lie. I once went to pick up a cavalier and was presented with the biggest springer I have ever seen. We often get told 'recall is great, really well trained no problems, our lives have just changed and we don't have time', when it's clear that the dog hasn't been trained at all. I had one that didn't even know the name we had been given and had no chip at 9 months old. We have no clue where they got him or where he had been since he was born or even if they had been the owner long. There had to be loads of extra steps to see if he had been stolen to reunite.
Also going to pick them up can be fairly upsetting.
In short, I know this is long. Don't commit to a rescue unless you are really sure you can handle anything. Fostering is good but risky and a big commitment. Puppies, in my experience, aren't that bad (only my exeprience) but you will what ages to get one from a rescue.
If you go through a breeder, do lots of research. Stay away from any that breed many puppies or have many breeds available. Lucy's law means that the breeder should own mum too, but there's a big loop hole in Lucy's law so puppy farms can still continue. So pointless really. The breeder, should quiz you to make sure you are right for them. But always double check anything they tell you about the breed. Don't ever buy from someone trying to rehome a dog around 10-26 weeks on Facebook, free ads, through a friend of a friend etc. Often there's huge problems and they don't want to surrender as they won't get any money back or is a scam.
My very first cocker was sold to me under the pretense of being like a cavalier. They are not the same. But I was young (19) and dumb assumed a breeder wouldn't lie 
Sorry its long. Just wanted to explain my experience. Other people's will be very different.